# Colb Liquids

## Overview

Colb Liquids is a system designed for the maintenance and management of diverse real-world assets (RWAs), enabling users to gain exposure to off-chain asset performance through the deposit of $USC tokens. When users deposit $USC, they receive liquid tokens that represent and track the value of specific RWAs.

Rather than distributing explicit yield, asset performance is reflected through the movement of the liquid token price over time, directly mirroring the underlying RWA's off-chain value changes.

The system relies on custom oracle infrastructure to deliver accurate, transparent asset pricing, while deposits and redemptions are managed through queue-based mechanisms designed to ensure orderly processing and liquidity control.

***

### What Are Colb Tokens?

Colb Tokens are native Swiss-structured, tokenized certificates that provide investors with on-chain exposure to the value of premium underlying Real-World Assets (RWAs), without custody constraints, intermediaries, or private banking barriers.

Each liquid token represents a proportional economic interest in a defined RWA. Token holders are exposed to changes in the USD-denominated value of the underlying assets through movements in the token price.

Liquid tokens do not distribute explicit yield. Instead, performance of the underlying RWA strategy is reflected directly through appreciation or depreciation of the token price over time.

***

### NAV

Net Asset Value (NAV) represents the net economic value of an RWA strategy at a given point in time. NAV is calculated as the total USD value of all underlying assets held by the strategy, net of accrued fees, expenses, and liabilities.

NAV serves as the core valuation reference within the protocol and is used to:

* Determine the liquid token rate
* Price deposits and redemptions
* Validate oracle price updates and transaction execution

Changes in NAV result from:

* Appreciation or depreciation of underlying assets
* Accrued interest or income
* Accumulation of management or performance fees
* Asset maturities, settlements, or redemptions

NAV is expressed in USD and allocated proportionally across the total liquid token supply or total shares held.

***

#### Token Rate Explained

The liquid token rate represents the **NAV per token** and is used to determine exchange values between USD (via $USC) and liquid tokens across all protocol operations, including deposits and redemptions.

$$
p = \frac{\Sigma - \varphi}{\tau}
$$

Where:

* **p** - Token rate 
* **Σ (Sigma)** - Total value of underlying RWA assets (USD)
* **φ (Phi)** - Accrued fees and expenses (USD)
* **τ (Tau)** - Total token supply or total shares 

The token rate is derived by subtracting accrued fees from total asset value and allocating the resulting net value proportionally across the total token supply typically (not total underlying shares held), as each token fractionally owns the net assets.

In cases where the Trust holds pre-IPO shares or other illiquid assets, the net asset value (after deducting accrued fees and expenses) is allocated proportionally across all outstanding tokens, with the token rate serving as a per-token representation of the underlying asset's estimated fair market value (e.g., pre-IPO pricing). Upon IPO or liquidity event, this rate transitions to reflect the official post-IPO price, adjusted for any applicable fee deductions to ensure accurate and transparent redemption values

***

#### Illustrative NAV Evolution for liquid RWAs

**Initial State (Day 0)**

| Symbol | Description           | Value             |
| ------ | --------------------- | ----------------- |
| Σ      | Total RWA Asset Value | USD 10,000,000    |
| φ      | Accrued Fees          | USD 0             |
| τ      | Total Token Supply    | 10,000,000 tokens |

$$
p\_0 = \frac{10{,}000{,}000 - 0}{10{,}000{,}000} = 1.0000
$$

***

**Subsequent State (Day 30)**

During the period:

* The RWA portfolio appreciates by **6.0%**.
* **USD 65,000** in management fees accrue.
* Token supply remains unchanged.

| Symbol | Description           | Value             |
| ------ | --------------------- | ----------------- |
| Σ      | Total RWA Asset Value | USD 10,600,000    |
| φ      | Accrued Fees          | USD 65,000        |
| τ      | Total Token Supply    | 10,000,000 tokens |

$$
p\_{30} = \frac{10{,}600{,}000 - 65{,}000}{10{,}000{,}000} = 1.0535
$$

Each token’s redemption value increases by approximately **5.35%**, reflecting net asset appreciation after fees.


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